CH_09_MULTICRITERIA_DECISION_MAKING

Scoring Model Overview

Each decision alternative graded in terms of how well it satisfies the
criterion according to following formula:

Si = Σgijwj

where:

wj = a weight between 0 and 1.00 assigned to criterion j;
1.00 important, 0 unimportant;

sum of total weights equals one.

gij = a grade between 0 and 100 indicating how well alternative i
satisfies criteria j;

100 indicates high satisfaction, 0 low satisfaction.

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Scoring Model
Example Problem

Mall selection with four alternatives and five criteria:

Grades for Alternative (0 to 100)

Weight

Decision Criteria (0 to 1.00) Mall 1 Mall 2 Mall 3 Mall 4

School proximity 0.30 40 60 90 60

Median income 0.25 75 80 65 90

Vehicular traffic 0.25 60 90 79 85

Mall quality, size 0.10 90 100 80 90

Other shopping 0.10 80 30 50 70

S1 = (.30)(40) + (.25)(75) + (.25)(60) + (.10)(90) + (.10)(80) = 62.75
S2 = (.30)(60) + (.25)(80) + (.25)(90) + (.10)(100) + (.10)(30) = 73.50
S3 = (.30)(90) + (.25)(65) + (.25)(79) + (.10)(80) + (.10)(50) = 76.00

S4 = (.30)(60) + (.25)(90) + (.25)(85) + (.10)(90) + (.10)(70) = 77.75

Mall 4 preferred because of highest score, followed by malls 3, 2, 1.

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Scoring Model
Excel Solution

Exhibit 9.16

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Goal Programming Example Problem
Problem Statement

Public relations firm survey interviewer staffing requirements
determination.

■ One person can conduct 80 telephone interviews or 40 personal
interviews per day.

■ $50/ day for telephone interviewer; $70 for personal interviewer.

■ Goals (in priority order):

1. At least 3,000 total interviews.

2. Interviewer conducts only one type of interview each day;
maintain daily budget of $2,500.

3. At least 1,000 interviews should be by telephone.

Formulate and solve a goal programming model to determine
number of interviewers to hire in order to satisfy the goals

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Goal Programming Example Problem 9-55
Solution (1 of 2)

Step 1: Model Formulation:
Minimize P1d1-, P2d2+, P3d3-
subject to:

80x1 + 40x2 + d1- - d1+ = 3,000 interviews
50x1 + 70x2 + d2- - d2 + = $2,500 budget
80x1 + d3- - d3 + = 1,000 telephone interviews
where:
x1 = number of telephone interviews
x2 = number of personal interviews

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Goal Programming Example Problem
Solution (2 of 2)

Step 2: QM for Windows Solution:

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Analytical Hierarchy Process Example Problem
Problem Statement

Purchasing decision, three model alternatives, three decision criteria.
Pairwise comparison matrices:

Price Bike Gear Action Bike Weight/Durability
Bike X Y Z X X
Y XY Z Y XYZ
X 136 Z 1 1/3 1/7 Z 131
Y 1/3 1 2 3 1 1/4 1/3 1 1/2
Z 1/6 1/2 1 74 1 121

Prioritized decision criteria:

Criteria Price Gears Weight

Price 1 3 5
Gears 1/3 1 2
Weight 1/5 1/2 1

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Analytical Hierarchy Process Example Problem
Problem Solution (1 of 4)

Step 1: Develop normalized matrices and preference vectors for all
the pairwise comparison matrices for criteria.

Bike X Price Z Row Averages

X 0.6667 Y 0.6667 0.6667
Y 0.2222 0.2222 0.2222
Z 0.1111 0.6667 0.1111 0.1111
0.2222 1.0000
0.1111

Bike X Gear Action Z Row Averages

X 0.0909 Y 0.1026 0.0853
Y 0.2727 0.0625 0.1795 0.2132
Z 0.6364 0.1875 0.7179 0.7014
0.7500 1.0000

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Analytical Hierarchy Process Example Problem
Problem Solution (2 of 4)

Step 1 continued: Develop normalized matrices and preference
vectors for all the pairwise comparison matrices for criteria.

Weight/Durability

Bike X Y Z Row Averages

X 0.4286 0.5000 0.4000 0.4429
Y 0.1429 0.1667 0.2000 0.1698
Z 0.4286 0.3333 0.4000 0.3873
1.0000

Bike Price Criteria Weight

X 0.6667 Gears 0.4429
Y 0.2222 0.1698
Z 0.1111 0.0853 0.3873
0.2132
0.7014

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Analytical Hierarchy Process Example Problem
Problem Solution (3 of 4)

Step 2: Rank the criteria.

Criteria Price Gears Weight Row Averages

Price 0.6522 0.6667 0.6250 0.6479
Gears 0.2174 0.2222 0.2500 0.2299
Weight 0.1304 0.1111 0.1250 0.1222
1.0000

Price 0.6479
Gears
Weight 

0.2299



0.1222



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Analytical Hierarchy Process Example Problem
Problem Solution (4 of 4)

Step 3: Develop an overall ranking.

Bike X 0.6667 0.0853 0.4429 0.6479
Bike Y  0.2132  
Bike Z 0.2222 0.7014
 0.1698 • 0.2299
  
 0.1111
 0.3837 0.1222
  

Bike X score = .6667(.6479) + .0853(.2299) + .4429(.1222) = .5057
Bike Y score = .2222(.6479) + .2132(.2299) + .1698(.1222) = .2138
Bike Z score = .1111(.6479) + .7014(.2299) + .3873(.1222) = .2806

Overall ranking of bikes: X first followed by Z and Y (sum of
scores equal 1.0000).

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